The probability of picking a red ball from the box at random is 1/4. Jack picks 4 balls from the box. We need to determine the probability that at least one of the balls picked will be red.
It is important to notice what the question asks, "what is the probability that at least one of the balls picked is red." The number of red balls picked can be 2, 3 or 4, but that is irrelevant. The required condition is is not fulfilled if none of the balls picked is red.
The probability of not picking a red ball is 1 - 1/4 = 3/4. For four balls, the probability is (3/4)(3/4)(3/4)(3/4) = 81/256.
This gives the probability that at least one ball picked is red as 1 - 81/256 = 175/256.
The required probability is 175/256